Properties

Label 138.6.d.a.137.10
Level $138$
Weight $6$
Character 138.137
Analytic conductor $22.133$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [138,6,Mod(137,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.137");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 138.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(22.1329671342\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 137.10
Character \(\chi\) \(=\) 138.137
Dual form 138.6.d.a.137.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000i q^{2} +(-15.1862 + 3.51856i) q^{3} -16.0000 q^{4} +0.0328033 q^{5} +(14.0742 + 60.7447i) q^{6} -156.501i q^{7} +64.0000i q^{8} +(218.240 - 106.867i) q^{9} +O(q^{10})\) \(q-4.00000i q^{2} +(-15.1862 + 3.51856i) q^{3} -16.0000 q^{4} +0.0328033 q^{5} +(14.0742 + 60.7447i) q^{6} -156.501i q^{7} +64.0000i q^{8} +(218.240 - 106.867i) q^{9} -0.131213i q^{10} +514.521 q^{11} +(242.979 - 56.2969i) q^{12} +415.779 q^{13} -626.004 q^{14} +(-0.498157 + 0.115420i) q^{15} +256.000 q^{16} -1767.95 q^{17} +(-427.467 - 872.958i) q^{18} -327.569i q^{19} -0.524853 q^{20} +(550.657 + 2376.65i) q^{21} -2058.08i q^{22} +(1263.99 - 2199.70i) q^{23} +(-225.188 - 971.915i) q^{24} -3125.00 q^{25} -1663.11i q^{26} +(-2938.21 + 2390.79i) q^{27} +2504.01i q^{28} -1444.40i q^{29} +(0.461681 + 1.99263i) q^{30} -8826.33 q^{31} -1024.00i q^{32} +(-7813.60 + 1810.37i) q^{33} +7071.80i q^{34} -5.13375i q^{35} +(-3491.83 + 1709.87i) q^{36} +1692.05i q^{37} -1310.28 q^{38} +(-6314.09 + 1462.94i) q^{39} +2.09941i q^{40} -12287.7i q^{41} +(9506.60 - 2202.63i) q^{42} +21379.8i q^{43} -8232.33 q^{44} +(7.15898 - 3.50559i) q^{45} +(-8798.79 - 5055.96i) q^{46} +972.502i q^{47} +(-3887.66 + 900.751i) q^{48} -7685.53 q^{49} +12500.0i q^{50} +(26848.4 - 6220.64i) q^{51} -6652.46 q^{52} -16242.2 q^{53} +(9563.14 + 11752.8i) q^{54} +16.8780 q^{55} +10016.1 q^{56} +(1152.57 + 4974.52i) q^{57} -5777.60 q^{58} -7885.38i q^{59} +(7.97051 - 1.84673i) q^{60} -33942.2i q^{61} +35305.3i q^{62} +(-16724.8 - 34154.7i) q^{63} -4096.00 q^{64} +13.6389 q^{65} +(7241.48 + 31254.4i) q^{66} +66229.6i q^{67} +28287.2 q^{68} +(-11455.4 + 37852.4i) q^{69} -20.5350 q^{70} -44256.3i q^{71} +(6839.48 + 13967.3i) q^{72} -36769.5 q^{73} +6768.20 q^{74} +(47456.8 - 10995.5i) q^{75} +5241.11i q^{76} -80522.9i q^{77} +(5851.76 + 25256.3i) q^{78} -19660.7i q^{79} +8.39765 q^{80} +(36208.0 - 46645.1i) q^{81} -49150.7 q^{82} -65271.3 q^{83} +(-8810.52 - 38026.4i) q^{84} -57.9946 q^{85} +85519.1 q^{86} +(5082.21 + 21934.9i) q^{87} +32929.3i q^{88} -116522. q^{89} +(-14.0223 - 28.6359i) q^{90} -65069.7i q^{91} +(-20223.8 + 35195.2i) q^{92} +(134038. - 31056.0i) q^{93} +3890.01 q^{94} -10.7454i q^{95} +(3603.00 + 15550.6i) q^{96} -126143. i q^{97} +30742.1i q^{98} +(112289. - 54985.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) −15.1862 + 3.51856i −0.974193 + 0.225716i
\(4\) −16.0000 −0.500000
\(5\) 0.0328033 0.000586803 0.000293402 1.00000i \(-0.499907\pi\)
0.000293402 1.00000i \(0.499907\pi\)
\(6\) 14.0742 + 60.7447i 0.159605 + 0.688859i
\(7\) 156.501i 1.20718i −0.797295 0.603590i \(-0.793737\pi\)
0.797295 0.603590i \(-0.206263\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 218.240 106.867i 0.898105 0.439781i
\(10\) 0.131213i 0.000414933i
\(11\) 514.521 1.28210 0.641049 0.767500i \(-0.278500\pi\)
0.641049 + 0.767500i \(0.278500\pi\)
\(12\) 242.979 56.2969i 0.487097 0.112858i
\(13\) 415.779 0.682345 0.341172 0.940001i \(-0.389176\pi\)
0.341172 + 0.940001i \(0.389176\pi\)
\(14\) −626.004 −0.853605
\(15\) −0.498157 + 0.115420i −0.000571660 + 0.000132451i
\(16\) 256.000 0.250000
\(17\) −1767.95 −1.48371 −0.741853 0.670563i \(-0.766053\pi\)
−0.741853 + 0.670563i \(0.766053\pi\)
\(18\) −427.467 872.958i −0.310972 0.635056i
\(19\) 327.569i 0.208170i −0.994568 0.104085i \(-0.966809\pi\)
0.994568 0.104085i \(-0.0331915\pi\)
\(20\) −0.524853 −0.000293402
\(21\) 550.657 + 2376.65i 0.272479 + 1.17603i
\(22\) 2058.08i 0.906580i
\(23\) 1263.99 2199.70i 0.498223 0.867049i
\(24\) −225.188 971.915i −0.0798025 0.344429i
\(25\) −3125.00 −1.00000
\(26\) 1663.11i 0.482491i
\(27\) −2938.21 + 2390.79i −0.775662 + 0.631148i
\(28\) 2504.01i 0.603590i
\(29\) 1444.40i 0.318928i −0.987204 0.159464i \(-0.949023\pi\)
0.987204 0.159464i \(-0.0509766\pi\)
\(30\) 0.461681 + 1.99263i 9.36568e−5 + 0.000404225i
\(31\) −8826.33 −1.64959 −0.824795 0.565432i \(-0.808710\pi\)
−0.824795 + 0.565432i \(0.808710\pi\)
\(32\) 1024.00i 0.176777i
\(33\) −7813.60 + 1810.37i −1.24901 + 0.289389i
\(34\) 7071.80i 1.04914i
\(35\) 5.13375i 0.000708377i
\(36\) −3491.83 + 1709.87i −0.449052 + 0.219891i
\(37\) 1692.05i 0.203193i 0.994826 + 0.101597i \(0.0323951\pi\)
−0.994826 + 0.101597i \(0.967605\pi\)
\(38\) −1310.28 −0.147199
\(39\) −6314.09 + 1462.94i −0.664736 + 0.154016i
\(40\) 2.09941i 0.000207466i
\(41\) 12287.7i 1.14159i −0.821093 0.570795i \(-0.806635\pi\)
0.821093 0.570795i \(-0.193365\pi\)
\(42\) 9506.60 2202.63i 0.831576 0.192672i
\(43\) 21379.8i 1.76332i 0.471881 + 0.881662i \(0.343575\pi\)
−0.471881 + 0.881662i \(0.656425\pi\)
\(44\) −8232.33 −0.641049
\(45\) 7.15898 3.50559i 0.000527011 0.000258065i
\(46\) −8798.79 5055.96i −0.613096 0.352297i
\(47\) 972.502i 0.0642164i 0.999484 + 0.0321082i \(0.0102221\pi\)
−0.999484 + 0.0321082i \(0.989778\pi\)
\(48\) −3887.66 + 900.751i −0.243548 + 0.0564289i
\(49\) −7685.53 −0.457282
\(50\) 12500.0i 0.707107i
\(51\) 26848.4 6220.64i 1.44542 0.334896i
\(52\) −6652.46 −0.341172
\(53\) −16242.2 −0.794246 −0.397123 0.917765i \(-0.629991\pi\)
−0.397123 + 0.917765i \(0.629991\pi\)
\(54\) 9563.14 + 11752.8i 0.446289 + 0.548476i
\(55\) 16.8780 0.000752339
\(56\) 10016.1 0.426802
\(57\) 1152.57 + 4974.52i 0.0469873 + 0.202798i
\(58\) −5777.60 −0.225516
\(59\) 7885.38i 0.294912i −0.989069 0.147456i \(-0.952892\pi\)
0.989069 0.147456i \(-0.0471085\pi\)
\(60\) 7.97051 1.84673i 0.000285830 6.62253e-5i
\(61\) 33942.2i 1.16792i −0.811781 0.583962i \(-0.801502\pi\)
0.811781 0.583962i \(-0.198498\pi\)
\(62\) 35305.3i 1.16644i
\(63\) −16724.8 34154.7i −0.530895 1.08417i
\(64\) −4096.00 −0.125000
\(65\) 13.6389 0.000400402
\(66\) 7241.48 + 31254.4i 0.204629 + 0.883184i
\(67\) 66229.6i 1.80246i 0.433345 + 0.901228i \(0.357333\pi\)
−0.433345 + 0.901228i \(0.642667\pi\)
\(68\) 28287.2 0.741853
\(69\) −11455.4 + 37852.4i −0.289659 + 0.957130i
\(70\) −20.5350 −0.000500898
\(71\) 44256.3i 1.04191i −0.853585 0.520953i \(-0.825577\pi\)
0.853585 0.520953i \(-0.174423\pi\)
\(72\) 6839.48 + 13967.3i 0.155486 + 0.317528i
\(73\) −36769.5 −0.807571 −0.403786 0.914854i \(-0.632306\pi\)
−0.403786 + 0.914854i \(0.632306\pi\)
\(74\) 6768.20 0.143679
\(75\) 47456.8 10995.5i 0.974193 0.225716i
\(76\) 5241.11i 0.104085i
\(77\) 80522.9i 1.54772i
\(78\) 5851.76 + 25256.3i 0.108906 + 0.470039i
\(79\) 19660.7i 0.354430i −0.984172 0.177215i \(-0.943291\pi\)
0.984172 0.177215i \(-0.0567088\pi\)
\(80\) 8.39765 0.000146701
\(81\) 36208.0 46645.1i 0.613185 0.789939i
\(82\) −49150.7 −0.807226
\(83\) −65271.3 −1.03998 −0.519992 0.854171i \(-0.674065\pi\)
−0.519992 + 0.854171i \(0.674065\pi\)
\(84\) −8810.52 38026.4i −0.136240 0.588013i
\(85\) −57.9946 −0.000870644
\(86\) 85519.1 1.24686
\(87\) 5082.21 + 21934.9i 0.0719870 + 0.310697i
\(88\) 32929.3i 0.453290i
\(89\) −116522. −1.55931 −0.779655 0.626209i \(-0.784606\pi\)
−0.779655 + 0.626209i \(0.784606\pi\)
\(90\) −14.0223 28.6359i −0.000182480 0.000372653i
\(91\) 65069.7i 0.823712i
\(92\) −20223.8 + 35195.2i −0.249112 + 0.433524i
\(93\) 134038. 31056.0i 1.60702 0.372338i
\(94\) 3890.01 0.0454079
\(95\) 10.7454i 0.000122155i
\(96\) 3603.00 + 15550.6i 0.0399013 + 0.172215i
\(97\) 126143.i 1.36124i −0.732638 0.680618i \(-0.761711\pi\)
0.732638 0.680618i \(-0.238289\pi\)
\(98\) 30742.1i 0.323347i
\(99\) 112289. 54985.2i 1.15146 0.563842i
\(100\) 50000.0 0.500000
\(101\) 131351.i 1.28124i −0.767858 0.640621i \(-0.778677\pi\)
0.767858 0.640621i \(-0.221323\pi\)
\(102\) −24882.5 107394.i −0.236807 1.02206i
\(103\) 61325.3i 0.569569i 0.958592 + 0.284785i \(0.0919220\pi\)
−0.958592 + 0.284785i \(0.908078\pi\)
\(104\) 26609.8i 0.241245i
\(105\) 18.0634 + 77.9620i 0.000159892 + 0.000690096i
\(106\) 64968.7i 0.561616i
\(107\) −85774.2 −0.724264 −0.362132 0.932127i \(-0.617951\pi\)
−0.362132 + 0.932127i \(0.617951\pi\)
\(108\) 47011.3 38252.6i 0.387831 0.315574i
\(109\) 177193.i 1.42850i 0.699889 + 0.714251i \(0.253233\pi\)
−0.699889 + 0.714251i \(0.746767\pi\)
\(110\) 67.5119i 0.000531984i
\(111\) −5953.57 25695.8i −0.0458638 0.197949i
\(112\) 40064.2i 0.301795i
\(113\) 250367. 1.84451 0.922255 0.386583i \(-0.126345\pi\)
0.922255 + 0.386583i \(0.126345\pi\)
\(114\) 19898.1 4610.28i 0.143400 0.0332250i
\(115\) 41.4630 72.1574i 0.000292359 0.000508787i
\(116\) 23110.4i 0.159464i
\(117\) 90739.3 44432.9i 0.612817 0.300082i
\(118\) −31541.5 −0.208534
\(119\) 276686.i 1.79110i
\(120\) −7.38690 31.8820i −4.68284e−5 0.000202112i
\(121\) 103680. 0.643774
\(122\) −135769. −0.825848
\(123\) 43234.9 + 186603.i 0.257675 + 1.11213i
\(124\) 141221. 0.824795
\(125\) −205.021 −0.00117361
\(126\) −136619. + 66899.0i −0.766626 + 0.375399i
\(127\) −6066.05 −0.0333731 −0.0166866 0.999861i \(-0.505312\pi\)
−0.0166866 + 0.999861i \(0.505312\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −75226.0 324677.i −0.398010 1.71782i
\(130\) 54.5557i 0.000283127i
\(131\) 20196.3i 0.102824i 0.998678 + 0.0514118i \(0.0163721\pi\)
−0.998678 + 0.0514118i \(0.983628\pi\)
\(132\) 125018. 28965.9i 0.624505 0.144695i
\(133\) −51264.9 −0.251299
\(134\) 264918. 1.27453
\(135\) −96.3828 + 78.4257i −0.000455161 + 0.000370360i
\(136\) 113149.i 0.524569i
\(137\) −44141.1 −0.200929 −0.100464 0.994941i \(-0.532033\pi\)
−0.100464 + 0.994941i \(0.532033\pi\)
\(138\) 151410. + 45821.6i 0.676793 + 0.204820i
\(139\) 39732.6 0.174426 0.0872128 0.996190i \(-0.472204\pi\)
0.0872128 + 0.996190i \(0.472204\pi\)
\(140\) 82.1400i 0.000354188i
\(141\) −3421.81 14768.6i −0.0144946 0.0625592i
\(142\) −177025. −0.736739
\(143\) 213927. 0.874832
\(144\) 55869.3 27357.9i 0.224526 0.109945i
\(145\) 47.3811i 0.000187148i
\(146\) 147078.i 0.571039i
\(147\) 116714. 27042.0i 0.445481 0.103216i
\(148\) 27072.8i 0.101597i
\(149\) 134915. 0.497847 0.248923 0.968523i \(-0.419923\pi\)
0.248923 + 0.968523i \(0.419923\pi\)
\(150\) −43982.0 189827.i −0.159605 0.688858i
\(151\) −497213. −1.77460 −0.887299 0.461195i \(-0.847421\pi\)
−0.887299 + 0.461195i \(0.847421\pi\)
\(152\) 20964.4 0.0735994
\(153\) −385837. + 188935.i −1.33252 + 0.652506i
\(154\) −322092. −1.09440
\(155\) −289.533 −0.000967985
\(156\) 101025. 23407.1i 0.332368 0.0770079i
\(157\) 407744.i 1.32020i 0.751179 + 0.660098i \(0.229485\pi\)
−0.751179 + 0.660098i \(0.770515\pi\)
\(158\) −78642.6 −0.250620
\(159\) 246657. 57149.1i 0.773749 0.179274i
\(160\) 33.5906i 0.000103733i
\(161\) −344255. 197815.i −1.04668 0.601445i
\(162\) −186581. 144832.i −0.558571 0.433587i
\(163\) −168675. −0.497259 −0.248630 0.968599i \(-0.579980\pi\)
−0.248630 + 0.968599i \(0.579980\pi\)
\(164\) 196603.i 0.570795i
\(165\) −256.312 + 59.3861i −0.000732924 + 0.000169815i
\(166\) 261085.i 0.735380i
\(167\) 421063.i 1.16830i 0.811644 + 0.584152i \(0.198573\pi\)
−0.811644 + 0.584152i \(0.801427\pi\)
\(168\) −152106. + 35242.1i −0.415788 + 0.0963359i
\(169\) −198421. −0.534406
\(170\) 231.978i 0.000615638i
\(171\) −35006.3 71488.5i −0.0915494 0.186959i
\(172\) 342077.i 0.881662i
\(173\) 488824.i 1.24176i −0.783906 0.620880i \(-0.786775\pi\)
0.783906 0.620880i \(-0.213225\pi\)
\(174\) 87739.6 20328.8i 0.219696 0.0509025i
\(175\) 489065.i 1.20718i
\(176\) 131717. 0.320524
\(177\) 27745.2 + 119749.i 0.0665663 + 0.287301i
\(178\) 466088.i 1.10260i
\(179\) 14603.8i 0.0340669i −0.999855 0.0170335i \(-0.994578\pi\)
0.999855 0.0170335i \(-0.00542218\pi\)
\(180\) −114.544 + 56.0894i −0.000263506 + 0.000129033i
\(181\) 558410.i 1.26694i −0.773767 0.633471i \(-0.781630\pi\)
0.773767 0.633471i \(-0.218370\pi\)
\(182\) −260279. −0.582453
\(183\) 119427. + 515451.i 0.263619 + 1.13778i
\(184\) 140781. + 80895.3i 0.306548 + 0.176148i
\(185\) 55.5048i 0.000119234i
\(186\) −124224. 536153.i −0.263283 1.13633i
\(187\) −909647. −1.90226
\(188\) 15560.0i 0.0321082i
\(189\) 374160. + 459832.i 0.761909 + 0.936363i
\(190\) −42.9814 −8.63767e−5
\(191\) 10405.4 0.0206383 0.0103192 0.999947i \(-0.496715\pi\)
0.0103192 + 0.999947i \(0.496715\pi\)
\(192\) 62202.6 14412.0i 0.121774 0.0282144i
\(193\) −300737. −0.581156 −0.290578 0.956851i \(-0.593848\pi\)
−0.290578 + 0.956851i \(0.593848\pi\)
\(194\) −504572. −0.962540
\(195\) −207.123 + 47.9893i −0.000390069 + 9.03770e-5i
\(196\) 122968. 0.228641
\(197\) 589962.i 1.08308i −0.840676 0.541538i \(-0.817842\pi\)
0.840676 0.541538i \(-0.182158\pi\)
\(198\) −219941. 449155.i −0.398697 0.814204i
\(199\) 77744.8i 0.139168i −0.997576 0.0695838i \(-0.977833\pi\)
0.997576 0.0695838i \(-0.0221671\pi\)
\(200\) 200000.i 0.353553i
\(201\) −233032. 1.00577e6i −0.406843 1.75594i
\(202\) −525405. −0.905974
\(203\) −226050. −0.385003
\(204\) −429574. + 99530.2i −0.722708 + 0.167448i
\(205\) 403.077i 0.000669889i
\(206\) 245301. 0.402746
\(207\) 40777.6 615140.i 0.0661448 0.997810i
\(208\) 106439. 0.170586
\(209\) 168541.i 0.266895i
\(210\) 311.848 72.2535i 0.000487972 0.000113061i
\(211\) 408048. 0.630965 0.315482 0.948931i \(-0.397834\pi\)
0.315482 + 0.948931i \(0.397834\pi\)
\(212\) 259875. 0.397123
\(213\) 155718. + 672083.i 0.235175 + 1.01502i
\(214\) 343097.i 0.512132i
\(215\) 701.328i 0.00103472i
\(216\) −153010. 188045.i −0.223145 0.274238i
\(217\) 1.38133e6i 1.99135i
\(218\) 708773. 1.01010
\(219\) 558388. 129376.i 0.786731 0.182281i
\(220\) −270.048 −0.000376170
\(221\) −735076. −1.01240
\(222\) −102783. + 23814.3i −0.139971 + 0.0324306i
\(223\) 973166. 1.31046 0.655231 0.755428i \(-0.272571\pi\)
0.655231 + 0.755428i \(0.272571\pi\)
\(224\) −160257. −0.213401
\(225\) −681998. + 333959.i −0.898105 + 0.439781i
\(226\) 1.00147e6i 1.30427i
\(227\) 819626. 1.05573 0.527863 0.849330i \(-0.322994\pi\)
0.527863 + 0.849330i \(0.322994\pi\)
\(228\) −18441.1 79592.3i −0.0234937 0.101399i
\(229\) 633956.i 0.798860i −0.916764 0.399430i \(-0.869208\pi\)
0.916764 0.399430i \(-0.130792\pi\)
\(230\) −288.630 165.852i −0.000359767 0.000206729i
\(231\) 283325. + 1.22284e6i 0.349345 + 1.50778i
\(232\) 92441.6 0.112758
\(233\) 1.30840e6i 1.57888i 0.613825 + 0.789442i \(0.289630\pi\)
−0.613825 + 0.789442i \(0.710370\pi\)
\(234\) −177732. 362957.i −0.212190 0.433327i
\(235\) 31.9013i 3.76824e-5i
\(236\) 126166.i 0.147456i
\(237\) 69177.1 + 298570.i 0.0800003 + 0.345283i
\(238\) 1.10674e6 1.26650
\(239\) 403526.i 0.456959i 0.973549 + 0.228479i \(0.0733754\pi\)
−0.973549 + 0.228479i \(0.926625\pi\)
\(240\) −127.528 + 29.5476i −0.000142915 + 3.31127e-5i
\(241\) 63519.3i 0.0704470i −0.999379 0.0352235i \(-0.988786\pi\)
0.999379 0.0352235i \(-0.0112143\pi\)
\(242\) 414722.i 0.455217i
\(243\) −385737. + 835761.i −0.419059 + 0.907959i
\(244\) 543075.i 0.583962i
\(245\) −252.111 −0.000268334
\(246\) 746411. 172940.i 0.786394 0.182204i
\(247\) 136196.i 0.142044i
\(248\) 564885.i 0.583218i
\(249\) 991221. 229661.i 1.01315 0.234741i
\(250\) 820.083i 0.000829865i
\(251\) 252393. 0.252867 0.126434 0.991975i \(-0.459647\pi\)
0.126434 + 0.991975i \(0.459647\pi\)
\(252\) 267596. + 546475.i 0.265447 + 0.542087i
\(253\) 650349. 1.13179e6i 0.638771 1.11164i
\(254\) 24264.2i 0.0235983i
\(255\) 880.716 204.057i 0.000848175 0.000196518i
\(256\) 65536.0 0.0625000
\(257\) 708073.i 0.668722i 0.942445 + 0.334361i \(0.108520\pi\)
−0.942445 + 0.334361i \(0.891480\pi\)
\(258\) −1.29871e6 + 300904.i −1.21468 + 0.281435i
\(259\) 264807. 0.245290
\(260\) −218.223 −0.000200201
\(261\) −154358. 315225.i −0.140258 0.286431i
\(262\) 80785.1 0.0727073
\(263\) 809213. 0.721396 0.360698 0.932683i \(-0.382539\pi\)
0.360698 + 0.932683i \(0.382539\pi\)
\(264\) −115864. 500070.i −0.102315 0.441592i
\(265\) −532.797 −0.000466066
\(266\) 205059.i 0.177695i
\(267\) 1.76952e6 409989.i 1.51907 0.351961i
\(268\) 1.05967e6i 0.901228i
\(269\) 1.58306e6i 1.33388i −0.745110 0.666941i \(-0.767603\pi\)
0.745110 0.666941i \(-0.232397\pi\)
\(270\) 313.703 + 385.531i 0.000261884 + 0.000321848i
\(271\) 725411. 0.600013 0.300007 0.953937i \(-0.403011\pi\)
0.300007 + 0.953937i \(0.403011\pi\)
\(272\) −452595. −0.370926
\(273\) 228952. + 988160.i 0.185925 + 0.802455i
\(274\) 176564.i 0.142078i
\(275\) −1.60788e6 −1.28210
\(276\) 183286. 605639.i 0.144830 0.478565i
\(277\) −959637. −0.751463 −0.375732 0.926729i \(-0.622609\pi\)
−0.375732 + 0.926729i \(0.622609\pi\)
\(278\) 158930.i 0.123337i
\(279\) −1.92625e6 + 943242.i −1.48151 + 0.725459i
\(280\) 328.560 0.000250449
\(281\) −1.23577e6 −0.933626 −0.466813 0.884356i \(-0.654598\pi\)
−0.466813 + 0.884356i \(0.654598\pi\)
\(282\) −59074.3 + 13687.2i −0.0442360 + 0.0102493i
\(283\) 2.14356e6i 1.59100i −0.605956 0.795498i \(-0.707209\pi\)
0.605956 0.795498i \(-0.292791\pi\)
\(284\) 708100.i 0.520953i
\(285\) 37.8081 + 163.181i 2.75723e−5 + 0.000119003i
\(286\) 855707.i 0.618600i
\(287\) −1.92303e6 −1.37810
\(288\) −109432. 223477.i −0.0777431 0.158764i
\(289\) 1.70579e6 1.20138
\(290\) −189.524 −0.000132334
\(291\) 443841. + 1.91563e6i 0.307252 + 1.32611i
\(292\) 588312. 0.403786
\(293\) 2.46156e6 1.67510 0.837550 0.546361i \(-0.183987\pi\)
0.837550 + 0.546361i \(0.183987\pi\)
\(294\) −108168. 466855.i −0.0729844 0.315002i
\(295\) 258.667i 0.000173055i
\(296\) −108291. −0.0718396
\(297\) −1.51177e6 + 1.23011e6i −0.994475 + 0.809193i
\(298\) 539661.i 0.352031i
\(299\) 525540. 914588.i 0.339960 0.591626i
\(300\) −759308. + 175928.i −0.487096 + 0.112858i
\(301\) 3.34596e6 2.12865
\(302\) 1.98885e6i 1.25483i
\(303\) 462167. + 1.99472e6i 0.289196 + 1.24818i
\(304\) 83857.7i 0.0520426i
\(305\) 1113.42i 0.000685342i
\(306\) 755741. + 1.54335e6i 0.461391 + 0.942236i
\(307\) 600443. 0.363602 0.181801 0.983335i \(-0.441807\pi\)
0.181801 + 0.983335i \(0.441807\pi\)
\(308\) 1.28837e6i 0.773861i
\(309\) −215776. 931296.i −0.128561 0.554870i
\(310\) 1158.13i 0.000684469i
\(311\) 3.09189e6i 1.81269i −0.422541 0.906344i \(-0.638862\pi\)
0.422541 0.906344i \(-0.361138\pi\)
\(312\) −93628.2 404101.i −0.0544528 0.235020i
\(313\) 842295.i 0.485963i 0.970031 + 0.242982i \(0.0781255\pi\)
−0.970031 + 0.242982i \(0.921875\pi\)
\(314\) 1.63098e6 0.933520
\(315\) −548.627 1120.39i −0.000311531 0.000636197i
\(316\) 314570.i 0.177215i
\(317\) 3.07049e6i 1.71616i −0.513512 0.858082i \(-0.671656\pi\)
0.513512 0.858082i \(-0.328344\pi\)
\(318\) −228596. 986626.i −0.126766 0.547123i
\(319\) 743174.i 0.408897i
\(320\) −134.362 −7.33504e−5
\(321\) 1.30258e6 301801.i 0.705573 0.163478i
\(322\) −791262. + 1.37702e6i −0.425285 + 0.740117i
\(323\) 579126.i 0.308864i
\(324\) −579327. + 746322.i −0.306593 + 0.394970i
\(325\) −1.29931e6 −0.682344
\(326\) 674702.i 0.351615i
\(327\) −623465. 2.69089e6i −0.322435 1.39164i
\(328\) 786412. 0.403613
\(329\) 152197. 0.0775207
\(330\) 237.545 + 1025.25i 0.000120077 + 0.000518255i
\(331\) 1.70299e6 0.854362 0.427181 0.904166i \(-0.359507\pi\)
0.427181 + 0.904166i \(0.359507\pi\)
\(332\) 1.04434e6 0.519992
\(333\) 180824. + 369272.i 0.0893605 + 0.182489i
\(334\) 1.68425e6 0.826116
\(335\) 2172.55i 0.00105769i
\(336\) 140968. + 608422.i 0.0681198 + 0.294006i
\(337\) 1.30869e6i 0.627716i −0.949470 0.313858i \(-0.898378\pi\)
0.949470 0.313858i \(-0.101622\pi\)
\(338\) 793684.i 0.377882i
\(339\) −3.80211e6 + 880930.i −1.79691 + 0.416334i
\(340\) 927.914 0.000435322
\(341\) −4.54133e6 −2.11494
\(342\) −285954. + 140025.i −0.132200 + 0.0647352i
\(343\) 1.42752e6i 0.655158i
\(344\) −1.36831e6 −0.623429
\(345\) −375.775 + 1241.68i −0.000169973 + 0.000561647i
\(346\) −1.95530e6 −0.878057
\(347\) 165579.i 0.0738212i 0.999319 + 0.0369106i \(0.0117517\pi\)
−0.999319 + 0.0369106i \(0.988248\pi\)
\(348\) −81315.3 350958.i −0.0359935 0.155349i
\(349\) −703244. −0.309060 −0.154530 0.987988i \(-0.549386\pi\)
−0.154530 + 0.987988i \(0.549386\pi\)
\(350\) 1.95626e6 0.853604
\(351\) −1.22164e6 + 994038.i −0.529269 + 0.430661i
\(352\) 526869.i 0.226645i
\(353\) 2.81277e6i 1.20143i −0.799465 0.600713i \(-0.794883\pi\)
0.799465 0.600713i \(-0.205117\pi\)
\(354\) 478995. 110981.i 0.203153 0.0470694i
\(355\) 1451.75i 0.000611395i
\(356\) 1.86435e6 0.779655
\(357\) −973535. 4.20180e6i −0.404279 1.74488i
\(358\) −58415.1 −0.0240889
\(359\) 1.53783e6 0.629757 0.314879 0.949132i \(-0.398036\pi\)
0.314879 + 0.949132i \(0.398036\pi\)
\(360\) 224.357 + 458.175i 9.12398e−5 + 0.000186327i
\(361\) 2.36880e6 0.956665
\(362\) −2.23364e6 −0.895863
\(363\) −1.57451e6 + 364806.i −0.627160 + 0.145310i
\(364\) 1.04112e6i 0.411856i
\(365\) −1206.16 −0.000473886
\(366\) 2.06181e6 477710.i 0.804535 0.186407i
\(367\) 1.90400e6i 0.737909i 0.929448 + 0.368954i \(0.120284\pi\)
−0.929448 + 0.368954i \(0.879716\pi\)
\(368\) 323581. 563123.i 0.124556 0.216762i
\(369\) −1.31315e6 2.68166e6i −0.502050 1.02527i
\(370\) 222.019 8.43114e−5
\(371\) 2.54192e6i 0.958797i
\(372\) −2.14461e6 + 496895.i −0.803510 + 0.186169i
\(373\) 2.21342e6i 0.823745i −0.911242 0.411872i \(-0.864875\pi\)
0.911242 0.411872i \(-0.135125\pi\)
\(374\) 3.63859e6i 1.34510i
\(375\) 3113.48 721.377i 0.00114332 0.000264901i
\(376\) −62240.1 −0.0227039
\(377\) 600551.i 0.217619i
\(378\) 1.83933e6 1.49664e6i 0.662109 0.538751i
\(379\) 3.50556e6i 1.25360i 0.779180 + 0.626800i \(0.215636\pi\)
−0.779180 + 0.626800i \(0.784364\pi\)
\(380\) 171.926i 6.10776e-5i
\(381\) 92120.0 21343.7i 0.0325119 0.00753283i
\(382\) 41621.5i 0.0145935i
\(383\) 3.74107e6 1.30316 0.651581 0.758579i \(-0.274106\pi\)
0.651581 + 0.758579i \(0.274106\pi\)
\(384\) −57648.0 248810.i −0.0199506 0.0861073i
\(385\) 2641.42i 0.000908208i
\(386\) 1.20295e6i 0.410940i
\(387\) 2.28479e6 + 4.66591e6i 0.775477 + 1.58365i
\(388\) 2.01829e6i 0.680618i
\(389\) −5.57331e6 −1.86741 −0.933704 0.358045i \(-0.883444\pi\)
−0.933704 + 0.358045i \(0.883444\pi\)
\(390\) 191.957 + 828.492i 6.39062e−5 + 0.000275821i
\(391\) −2.23467e6 + 3.88896e6i −0.739216 + 1.28645i
\(392\) 491874.i 0.161673i
\(393\) −71061.8 306704.i −0.0232089 0.100170i
\(394\) −2.35985e6 −0.765850
\(395\) 644.934i 0.000207981i
\(396\) −1.79662e6 + 879763.i −0.575729 + 0.281921i
\(397\) −3.28582e6 −1.04633 −0.523164 0.852232i \(-0.675249\pi\)
−0.523164 + 0.852232i \(0.675249\pi\)
\(398\) −310979. −0.0984064
\(399\) 778517. 180378.i 0.244814 0.0567221i
\(400\) −800000. −0.250000
\(401\) −746282. −0.231762 −0.115881 0.993263i \(-0.536969\pi\)
−0.115881 + 0.993263i \(0.536969\pi\)
\(402\) −4.02309e6 + 932130.i −1.24164 + 0.287681i
\(403\) −3.66980e6 −1.12559
\(404\) 2.10162e6i 0.640621i
\(405\) 1187.74 1530.11i 0.000359819 0.000463539i
\(406\) 904200.i 0.272238i
\(407\) 870594.i 0.260513i
\(408\) 398121. + 1.71830e6i 0.118403 + 0.511032i
\(409\) −3.62534e6 −1.07162 −0.535809 0.844339i \(-0.679993\pi\)
−0.535809 + 0.844339i \(0.679993\pi\)
\(410\) −1612.31 −0.000473683
\(411\) 670334. 155313.i 0.195743 0.0453527i
\(412\) 981204.i 0.284785i
\(413\) −1.23407e6 −0.356012
\(414\) −2.46056e6 163110.i −0.705558 0.0467715i
\(415\) −2141.11 −0.000610267
\(416\) 425757.i 0.120623i
\(417\) −603386. + 139801.i −0.169924 + 0.0393706i
\(418\) −674164. −0.188723
\(419\) 330982. 0.0921020 0.0460510 0.998939i \(-0.485336\pi\)
0.0460510 + 0.998939i \(0.485336\pi\)
\(420\) −289.014 1247.39i −7.99458e−5 0.000345048i
\(421\) 96617.4i 0.0265675i −0.999912 0.0132837i \(-0.995772\pi\)
0.999912 0.0132837i \(-0.00422847\pi\)
\(422\) 1.63219e6i 0.446160i
\(423\) 103928. + 212238.i 0.0282412 + 0.0576731i
\(424\) 1.03950e6i 0.280808i
\(425\) 5.52484e6 1.48371
\(426\) 2.68833e6 622873.i 0.717727 0.166294i
\(427\) −5.31198e6 −1.40989
\(428\) 1.37239e6 0.362132
\(429\) −3.24873e6 + 752713.i −0.852256 + 0.197463i
\(430\) 2805.31 0.000731661
\(431\) 2.74215e6 0.711047 0.355523 0.934667i \(-0.384303\pi\)
0.355523 + 0.934667i \(0.384303\pi\)
\(432\) −752180. + 612041.i −0.193916 + 0.157787i
\(433\) 751889.i 0.192723i −0.995346 0.0963617i \(-0.969279\pi\)
0.995346 0.0963617i \(-0.0307205\pi\)
\(434\) 5.52532e6 1.40810
\(435\) 166.713 + 719.537i 4.22422e−5 + 0.000182318i
\(436\) 2.83509e6i 0.714251i
\(437\) −720553. 414044.i −0.180494 0.103715i
\(438\) −517503. 2.23355e6i −0.128892 0.556302i
\(439\) 6.44215e6 1.59540 0.797699 0.603055i \(-0.206050\pi\)
0.797699 + 0.603055i \(0.206050\pi\)
\(440\) 1080.19i 0.000265992i
\(441\) −1.67729e6 + 821328.i −0.410687 + 0.201104i
\(442\) 2.94030e6i 0.715874i
\(443\) 5.82910e6i 1.41121i 0.708605 + 0.705605i \(0.249325\pi\)
−0.708605 + 0.705605i \(0.750675\pi\)
\(444\) 95257.2 + 411132.i 0.0229319 + 0.0989746i
\(445\) −3822.30 −0.000915008
\(446\) 3.89266e6i 0.926637i
\(447\) −2.04885e6 + 474707.i −0.484999 + 0.112372i
\(448\) 641028.i 0.150897i
\(449\) 3.08357e6i 0.721835i −0.932598 0.360917i \(-0.882464\pi\)
0.932598 0.360917i \(-0.117536\pi\)
\(450\) 1.33583e6 + 2.72799e6i 0.310972 + 0.635056i
\(451\) 6.32226e6i 1.46363i
\(452\) −4.00587e6 −0.922255
\(453\) 7.55076e6 1.74947e6i 1.72880 0.400554i
\(454\) 3.27850e6i 0.746511i
\(455\) 2134.50i 0.000483357i
\(456\) −318369. + 73764.5i −0.0717000 + 0.0166125i
\(457\) 1.88406e6i 0.421993i 0.977487 + 0.210997i \(0.0676709\pi\)
−0.977487 + 0.210997i \(0.932329\pi\)
\(458\) −2.53583e6 −0.564879
\(459\) 5.19460e6 4.22679e6i 1.15085 0.936438i
\(460\) −663.409 + 1154.52i −0.000146180 + 0.000254394i
\(461\) 276893.i 0.0606820i 0.999540 + 0.0303410i \(0.00965933\pi\)
−0.999540 + 0.0303410i \(0.990341\pi\)
\(462\) 4.89134e6 1.13330e6i 1.06616 0.247024i
\(463\) −2.39789e6 −0.519848 −0.259924 0.965629i \(-0.583698\pi\)
−0.259924 + 0.965629i \(0.583698\pi\)
\(464\) 369766.i 0.0797320i
\(465\) 4396.90 1018.74i 0.000943005 0.000218489i
\(466\) 5.23359e6 1.11644
\(467\) −1.16343e6 −0.246860 −0.123430 0.992353i \(-0.539389\pi\)
−0.123430 + 0.992353i \(0.539389\pi\)
\(468\) −1.45183e6 + 710927.i −0.306409 + 0.150041i
\(469\) 1.03650e7 2.17589
\(470\) 127.605 2.66455e−5
\(471\) −1.43467e6 6.19207e6i −0.297989 1.28613i
\(472\) 504664. 0.104267
\(473\) 1.10003e7i 2.26075i
\(474\) 1.19428e6 276709.i 0.244152 0.0565688i
\(475\) 1.02365e6i 0.208170i
\(476\) 4.42697e6i 0.895549i
\(477\) −3.54469e6 + 1.73575e6i −0.713316 + 0.349294i
\(478\) 1.61411e6 0.323119
\(479\) 2.38466e6 0.474884 0.237442 0.971402i \(-0.423691\pi\)
0.237442 + 0.971402i \(0.423691\pi\)
\(480\) 118.190 + 510.112i 2.34142e−5 + 0.000101056i
\(481\) 703518.i 0.138648i
\(482\) −254077. −0.0498136
\(483\) 5.92394e6 + 1.79278e6i 1.15543 + 0.349670i
\(484\) −1.65889e6 −0.321887
\(485\) 4137.91i 0.000798778i
\(486\) 3.34304e6 + 1.54295e6i 0.642024 + 0.296320i
\(487\) −1.13750e6 −0.217335 −0.108668 0.994078i \(-0.534658\pi\)
−0.108668 + 0.994078i \(0.534658\pi\)
\(488\) 2.17230e6 0.412924
\(489\) 2.56153e6 593494.i 0.484426 0.112239i
\(490\) 1008.44i 0.000189741i
\(491\) 1.41268e6i 0.264448i 0.991220 + 0.132224i \(0.0422118\pi\)
−0.991220 + 0.132224i \(0.957788\pi\)
\(492\) −691759. 2.98564e6i −0.128837 0.556065i
\(493\) 2.55363e6i 0.473195i
\(494\) −544785. −0.100440
\(495\) 3683.44 1803.70i 0.000675680 0.000330865i
\(496\) −2.25954e6 −0.412398
\(497\) −6.92615e6 −1.25777
\(498\) −918643. 3.96488e6i −0.165987 0.716403i
\(499\) 6.71999e6 1.20814 0.604070 0.796931i \(-0.293545\pi\)
0.604070 + 0.796931i \(0.293545\pi\)
\(500\) 3280.33 0.000586803
\(501\) −1.48153e6 6.39434e6i −0.263704 1.13815i
\(502\) 1.00957e6i 0.178804i
\(503\) −7.30586e6 −1.28751 −0.643756 0.765231i \(-0.722625\pi\)
−0.643756 + 0.765231i \(0.722625\pi\)
\(504\) 2.18590e6 1.07038e6i 0.383313 0.187700i
\(505\) 4308.76i 0.000751837i
\(506\) −4.52716e6 2.60139e6i −0.786049 0.451679i
\(507\) 3.01326e6 698156.i 0.520614 0.120624i
\(508\) 97056.8 0.0166866
\(509\) 3.42230e6i 0.585496i −0.956190 0.292748i \(-0.905430\pi\)
0.956190 0.292748i \(-0.0945697\pi\)
\(510\) −816.230 3522.86i −0.000138959 0.000599750i
\(511\) 5.75446e6i 0.974883i
\(512\) 262144.i 0.0441942i
\(513\) 783148. + 962465.i 0.131386 + 0.161470i
\(514\) 2.83229e6 0.472858
\(515\) 2011.67i 0.000334225i
\(516\) 1.20362e6 + 5.19483e6i 0.199005 + 0.858909i
\(517\) 500373.i 0.0823317i
\(518\) 1.05923e6i 0.173446i
\(519\) 1.71996e6 + 7.42337e6i 0.280285 + 1.20971i
\(520\) 872.891i 0.000141564i
\(521\) 8.26650e6 1.33422 0.667110 0.744960i \(-0.267531\pi\)
0.667110 + 0.744960i \(0.267531\pi\)
\(522\) −1.26090e6 + 617434.i −0.202537 + 0.0991777i
\(523\) 5.11333e6i 0.817427i −0.912663 0.408714i \(-0.865977\pi\)
0.912663 0.408714i \(-0.134023\pi\)
\(524\) 323140.i 0.0514118i
\(525\) −1.72080e6 7.42703e6i −0.272479 1.17603i
\(526\) 3.23685e6i 0.510104i
\(527\) 1.56045e7 2.44751
\(528\) −2.00028e6 + 463455.i −0.312253 + 0.0723473i
\(529\) −3.24100e6 5.56079e6i −0.503548 0.863968i
\(530\) 2131.19i 0.000329558i
\(531\) −842686. 1.72090e6i −0.129697 0.264862i
\(532\) 820238. 0.125649
\(533\) 5.10895e6i 0.778958i
\(534\) −1.63996e6 7.07808e6i −0.248874 1.07414i
\(535\) −2813.68 −0.000425001
\(536\) −4.23869e6 −0.637265
\(537\) 51384.3 + 221776.i 0.00768943 + 0.0331878i
\(538\) −6.33226e6 −0.943198
\(539\) −3.95436e6 −0.586280
\(540\) 1542.13 1254.81i 0.000227581 0.000185180i
\(541\) 1.38456e6 0.203385 0.101693 0.994816i \(-0.467574\pi\)
0.101693 + 0.994816i \(0.467574\pi\)
\(542\) 2.90164e6i 0.424274i
\(543\) 1.96480e6 + 8.48011e6i 0.285968 + 1.23425i
\(544\) 1.81038e6i 0.262285i
\(545\) 5812.53i 0.000838250i
\(546\) 3.95264e6 915806.i 0.567421 0.131469i
\(547\) −7.02754e6 −1.00423 −0.502117 0.864800i \(-0.667445\pi\)
−0.502117 + 0.864800i \(0.667445\pi\)
\(548\) 706257. 0.100464
\(549\) −3.62729e6 7.40752e6i −0.513631 1.04892i
\(550\) 6.43151e6i 0.906580i
\(551\) −473141. −0.0663913
\(552\) −2.42255e6 733145.i −0.338397 0.102410i
\(553\) −3.07691e6 −0.427860
\(554\) 3.83855e6i 0.531365i
\(555\) −195.297 842.906i −2.69131e−5 0.000116157i
\(556\) −635722. −0.0872128
\(557\) −773371. −0.105621 −0.0528104 0.998605i \(-0.516818\pi\)
−0.0528104 + 0.998605i \(0.516818\pi\)
\(558\) 3.77297e6 + 7.70502e6i 0.512977 + 1.04758i
\(559\) 8.88926e6i 1.20320i
\(560\) 1314.24i 0.000177094i
\(561\) 1.38141e7 3.20065e6i 1.85316 0.429369i
\(562\) 4.94309e6i 0.660174i
\(563\) −5.10022e6 −0.678138 −0.339069 0.940762i \(-0.610112\pi\)
−0.339069 + 0.940762i \(0.610112\pi\)
\(564\) 54748.9 + 236297.i 0.00724732 + 0.0312796i
\(565\) 8212.86 0.00108236
\(566\) −8.57423e6 −1.12500
\(567\) −7.30000e6 5.66658e6i −0.953598 0.740224i
\(568\) 2.83240e6 0.368370
\(569\) 1.38405e7 1.79214 0.896068 0.443917i \(-0.146411\pi\)
0.896068 + 0.443917i \(0.146411\pi\)
\(570\) 652.723 151.233i 8.41476e−5 1.94966e-5i
\(571\) 2.31043e6i 0.296553i −0.988946 0.148277i \(-0.952627\pi\)
0.988946 0.148277i \(-0.0473726\pi\)
\(572\) −3.42283e6 −0.437416
\(573\) −158018. + 36611.9i −0.0201057 + 0.00465839i
\(574\) 7.69213e6i 0.974467i
\(575\) −3.94997e6 + 6.87406e6i −0.498223 + 0.867049i
\(576\) −893909. + 437727.i −0.112263 + 0.0549726i
\(577\) −6.82028e6 −0.852830 −0.426415 0.904528i \(-0.640224\pi\)
−0.426415 + 0.904528i \(0.640224\pi\)
\(578\) 6.82317e6i 0.849506i
\(579\) 4.56704e6 1.05816e6i 0.566159 0.131176i
\(580\) 758.098i 9.35740e-5i
\(581\) 1.02150e7i 1.25545i
\(582\) 7.66251e6 1.77536e6i 0.937700 0.217260i
\(583\) −8.35694e6 −1.01830
\(584\) 2.35325e6i 0.285520i
\(585\) 2976.55 1457.55i 0.000359603 0.000176089i
\(586\) 9.84622e6i 1.18447i
\(587\) 1.28259e7i 1.53636i −0.640233 0.768181i \(-0.721162\pi\)
0.640233 0.768181i \(-0.278838\pi\)
\(588\) −1.86742e6 + 432672.i −0.222740 + 0.0516078i
\(589\) 2.89123e6i 0.343396i
\(590\) −1034.67 −0.000122369
\(591\) 2.07582e6 + 8.95927e6i 0.244467 + 1.05512i
\(592\) 433165.i 0.0507983i
\(593\) 1.54759e6i 0.180726i −0.995909 0.0903628i \(-0.971197\pi\)
0.995909 0.0903628i \(-0.0288027\pi\)
\(594\) 4.92044e6 + 6.04707e6i 0.572186 + 0.703200i
\(595\) 9076.21i 0.00105102i
\(596\) −2.15864e6 −0.248923
\(597\) 273549. + 1.18065e6i 0.0314123 + 0.135576i
\(598\) −3.65835e6 2.10216e6i −0.418343 0.240388i
\(599\) 1.11713e7i 1.27215i 0.771627 + 0.636075i \(0.219443\pi\)
−0.771627 + 0.636075i \(0.780557\pi\)
\(600\) 703711. + 3.03723e6i 0.0798025 + 0.344429i
\(601\) −1.19470e7 −1.34918 −0.674592 0.738191i \(-0.735680\pi\)
−0.674592 + 0.738191i \(0.735680\pi\)
\(602\) 1.33838e7i 1.50518i
\(603\) 7.07774e6 + 1.44539e7i 0.792686 + 1.61880i
\(604\) 7.95540e6 0.887299
\(605\) 3401.06 0.000377769
\(606\) 7.97889e6 1.84867e6i 0.882594 0.204493i
\(607\) 181705. 0.0200168 0.0100084 0.999950i \(-0.496814\pi\)
0.0100084 + 0.999950i \(0.496814\pi\)
\(608\) −335431. −0.0367997
\(609\) 3.43283e6 795370.i 0.375067 0.0869012i
\(610\) −4453.66 −0.000484610
\(611\) 404346.i 0.0438177i
\(612\) 6.17339e6 3.02296e6i 0.666262 0.326253i
\(613\) 2.64180e6i 0.283954i 0.989870 + 0.141977i \(0.0453460\pi\)
−0.989870 + 0.141977i \(0.954654\pi\)
\(614\) 2.40177e6i 0.257105i
\(615\) 1418.25 + 6121.19i 0.000151204 + 0.000652601i
\(616\) 5.15347e6 0.547202
\(617\) 4.66150e6 0.492961 0.246481 0.969148i \(-0.420726\pi\)
0.246481 + 0.969148i \(0.420726\pi\)
\(618\) −3.72518e6 + 863106.i −0.392353 + 0.0909061i
\(619\) 1.13068e6i 0.118608i 0.998240 + 0.0593038i \(0.0188881\pi\)
−0.998240 + 0.0593038i \(0.981112\pi\)
\(620\) 4632.53 0.000483993
\(621\) 1.54515e6 + 9.48509e6i 0.160783 + 0.986990i
\(622\) −1.23676e7 −1.28176
\(623\) 1.82358e7i 1.88237i
\(624\) −1.61641e6 + 374513.i −0.166184 + 0.0385040i
\(625\) 9.76561e6 0.999999
\(626\) 3.36918e6 0.343628
\(627\) 593022. + 2.55949e6i 0.0602423 + 0.260007i
\(628\) 6.52390e6i 0.660098i
\(629\) 2.99146e6i 0.301479i
\(630\) −4481.55 + 2194.51i −0.000449859 + 0.000220286i
\(631\) 1.30238e7i 1.30216i −0.759010 0.651079i \(-0.774317\pi\)
0.759010 0.651079i \(-0.225683\pi\)
\(632\) 1.25828e6 0.125310
\(633\) −6.19669e6 + 1.43574e6i −0.614682 + 0.142419i
\(634\) −1.22819e7 −1.21351
\(635\) −198.986 −1.95835e−5
\(636\) −3.94651e6 + 914385.i −0.386874 + 0.0896368i
\(637\) −3.19548e6 −0.312024
\(638\) −2.97269e6 −0.289134
\(639\) −4.72953e6 9.65847e6i −0.458211 0.935742i
\(640\) 537.449i 5.18666e-5i
\(641\) 7.86815e6 0.756358 0.378179 0.925733i \(-0.376550\pi\)
0.378179 + 0.925733i \(0.376550\pi\)
\(642\) −1.20721e6 5.21033e6i −0.115596 0.498916i
\(643\) 1.56004e7i 1.48802i 0.668169 + 0.744009i \(0.267078\pi\)
−0.668169 + 0.744009i \(0.732922\pi\)
\(644\) 5.50808e6 + 3.16505e6i 0.523342 + 0.300722i
\(645\) −2467.66 10650.5i −0.000233554 0.00100802i
\(646\) 2.31650e6 0.218400
\(647\) 1.61792e6i 0.151949i −0.997110 0.0759744i \(-0.975793\pi\)
0.997110 0.0759744i \(-0.0242067\pi\)
\(648\) 2.98529e6 + 2.31731e6i 0.279286 + 0.216794i
\(649\) 4.05719e6i 0.378106i
\(650\) 5.19723e6i 0.482490i
\(651\) −4.86029e6 2.09771e7i −0.449479 1.93996i
\(652\) 2.69881e6 0.248630
\(653\) 1.13742e7i 1.04385i 0.852992 + 0.521925i \(0.174786\pi\)
−0.852992 + 0.521925i \(0.825214\pi\)
\(654\) −1.07636e7 + 2.49386e6i −0.984037 + 0.227996i
\(655\) 662.505i 6.03373e-5i
\(656\) 3.14565e6i 0.285398i
\(657\) −8.02456e6 + 3.92944e6i −0.725284 + 0.355155i
\(658\) 608790.i 0.0548154i
\(659\) −1.82620e7 −1.63808 −0.819040 0.573736i \(-0.805494\pi\)
−0.819040 + 0.573736i \(0.805494\pi\)
\(660\) 4100.99 950.178i 0.000366462 8.49073e-5i
\(661\) 1.36419e7i 1.21443i 0.794538 + 0.607215i \(0.207713\pi\)
−0.794538 + 0.607215i \(0.792287\pi\)
\(662\) 6.81196e6i 0.604125i
\(663\) 1.11630e7 2.58641e6i 0.986272 0.228514i
\(664\) 4.17736e6i 0.367690i
\(665\) −1681.66 −0.000147463
\(666\) 1.47709e6 723296.i 0.129039 0.0631874i
\(667\) −3.17724e6 1.82571e6i −0.276526 0.158897i
\(668\) 6.73701e6i 0.584152i
\(669\) −1.47787e7 + 3.42414e6i −1.27664 + 0.295792i
\(670\) 8690.19 0.000747898
\(671\) 1.74639e7i 1.49739i
\(672\) 2.43369e6 563873.i 0.207894 0.0481680i
\(673\) −5.50902e6 −0.468853 −0.234426 0.972134i \(-0.575321\pi\)
−0.234426 + 0.972134i \(0.575321\pi\)
\(674\) −5.23477e6 −0.443862
\(675\) 9.18189e6 7.47120e6i 0.775662 0.631148i
\(676\) 3.17474e6 0.267203
\(677\) 1.22229e7 1.02495 0.512476 0.858702i \(-0.328729\pi\)
0.512476 + 0.858702i \(0.328729\pi\)
\(678\) 3.52372e6 + 1.52085e7i 0.294393 + 1.27061i
\(679\) −1.97415e7 −1.64326
\(680\) 3711.66i 0.000307819i
\(681\) −1.24470e7 + 2.88390e6i −1.02848 + 0.238294i
\(682\) 1.81653e7i 1.49549i
\(683\) 2.02081e7i 1.65758i −0.559561 0.828789i \(-0.689030\pi\)
0.559561 0.828789i \(-0.310970\pi\)
\(684\) 560100. + 1.14382e6i 0.0457747 + 0.0934794i
\(685\) −1447.97 −0.000117906
\(686\) −5.71007e6 −0.463267
\(687\) 2.23061e6 + 9.62737e6i 0.180315 + 0.778244i
\(688\) 5.47323e6i 0.440831i
\(689\) −6.75315e6 −0.541949
\(690\) 4966.74 + 1503.10i 0.000397144 + 0.000120189i
\(691\) 1.15788e7 0.922507 0.461253 0.887269i \(-0.347400\pi\)
0.461253 + 0.887269i \(0.347400\pi\)
\(692\) 7.82119e6i 0.620880i
\(693\) −8.60523e6 1.75733e7i −0.680659 1.39002i
\(694\) 662315. 0.0521995
\(695\) 1303.36 0.000102354
\(696\) −1.40383e6 + 325261.i −0.109848 + 0.0254512i
\(697\) 2.17240e7i 1.69378i
\(698\) 2.81298e6i 0.218538i
\(699\) −4.60367e6 1.98696e7i −0.356379 1.53814i
\(700\) 7.82504e6i 0.603589i
\(701\) 1.22850e7 0.944234 0.472117 0.881536i \(-0.343490\pi\)
0.472117 + 0.881536i \(0.343490\pi\)
\(702\) 3.97615e6 + 4.88657e6i 0.304523 + 0.374250i
\(703\) 554263. 0.0422988
\(704\) −2.10748e6 −0.160262
\(705\) −112.247 484.458i −8.50551e−6 3.67099e-5i
\(706\) −1.12511e7 −0.849536
\(707\) −2.05566e7 −1.54669
\(708\) −443923. 1.91598e6i −0.0332831 0.143651i
\(709\) 2.44045e6i 0.182328i 0.995836 + 0.0911642i \(0.0290588\pi\)
−0.995836 + 0.0911642i \(0.970941\pi\)
\(710\) −5807.01 −0.000432321
\(711\) −2.10107e6 4.29073e6i −0.155872 0.318315i
\(712\) 7.45740e6i 0.551299i
\(713\) −1.11564e7 + 1.94153e7i −0.821864 + 1.43028i
\(714\) −1.68072e7 + 3.89414e6i −1.23381 + 0.285868i
\(715\) 7017.50 0.000513355
\(716\) 233661.i 0.0170335i
\(717\) −1.41983e6 6.12802e6i −0.103143 0.445166i
\(718\) 6.15133e6i 0.445306i
\(719\) 8.55273e6i 0.616996i −0.951225 0.308498i \(-0.900174\pi\)
0.951225 0.308498i \(-0.0998264\pi\)
\(720\) 1832.70 897.430i 0.000131753 6.45163e-5i
\(721\) 9.59746e6 0.687572
\(722\) 9.47519e6i 0.676464i
\(723\) 223496. + 964614.i 0.0159010 + 0.0686290i
\(724\) 8.93456e6i 0.633471i
\(725\) 4.51375e6i 0.318928i
\(726\) 1.45922e6 + 6.29804e6i 0.102750 + 0.443469i
\(727\) 6.59873e6i 0.463046i −0.972829 0.231523i \(-0.925629\pi\)
0.972829 0.231523i \(-0.0743708\pi\)
\(728\) 4.16446e6 0.291226
\(729\) 2.91719e6 1.40492e7i 0.203304 0.979116i
\(730\) 4824.65i 0.000335088i
\(731\) 3.77984e7i 2.61625i
\(732\) −1.91084e6 8.24722e6i −0.131809 0.568892i
\(733\) 4.60639e6i 0.316665i 0.987386 + 0.158333i \(0.0506119\pi\)
−0.987386 + 0.158333i \(0.949388\pi\)
\(734\) 7.61602e6 0.521780
\(735\) 3828.60 887.067i 0.000261410 6.05672e-5i
\(736\) −2.25249e6 1.29433e6i −0.153274 0.0880742i
\(737\) 3.40765e7i 2.31093i
\(738\) −1.07266e7 + 5.25258e6i −0.724974 + 0.355003i
\(739\) −832395. −0.0560684 −0.0280342 0.999607i \(-0.508925\pi\)
−0.0280342 + 0.999607i \(0.508925\pi\)
\(740\) 888.077i 5.96172e-5i
\(741\) 479214. + 2.06830e6i 0.0320615 + 0.138378i
\(742\) 1.01677e7 0.677972
\(743\) 1.12065e7 0.744728 0.372364 0.928087i \(-0.378547\pi\)
0.372364 + 0.928087i \(0.378547\pi\)
\(744\) 1.98758e6 + 8.57845e6i 0.131641 + 0.568167i
\(745\) 4425.67 0.000292138
\(746\) −8.85370e6 −0.582476
\(747\) −1.42448e7 + 6.97534e6i −0.934015 + 0.457366i
\(748\) 1.45544e7 0.951128
\(749\) 1.34237e7i 0.874317i
\(750\) −2885.51 12453.9i −0.000187314 0.000808449i
\(751\) 1.68641e7i 1.09109i −0.838080 0.545547i \(-0.816322\pi\)
0.838080 0.545547i \(-0.183678\pi\)
\(752\) 248961.i 0.0160541i
\(753\) −3.83288e6 + 888058.i −0.246341 + 0.0570761i
\(754\) −2.40220e6 −0.153880
\(755\) −16310.2 −0.00104134
\(756\) −5.98656e6 7.35731e6i −0.380954 0.468182i
\(757\) 1.67223e7i 1.06061i −0.847807 0.530305i \(-0.822077\pi\)
0.847807 0.530305i \(-0.177923\pi\)
\(758\) 1.40222e7 0.886429
\(759\) −5.89404e6 + 1.94758e7i −0.371371 + 1.22713i
\(760\) 687.702 4.31883e−5
\(761\) 2.59693e7i 1.62554i 0.582582 + 0.812772i \(0.302042\pi\)
−0.582582 + 0.812772i \(0.697958\pi\)
\(762\) −85375.0 368480.i −0.00532651 0.0229893i
\(763\) 2.77309e7 1.72446
\(764\) −166486. −0.0103192
\(765\) −12656.7 + 6197.70i −0.000781929 + 0.000382893i
\(766\) 1.49643e7i 0.921475i
\(767\) 3.27857e6i 0.201232i
\(768\) −995241. + 230592.i −0.0608871 + 0.0141072i
\(769\) 1.01967e7i 0.621793i −0.950444 0.310896i \(-0.899371\pi\)
0.950444 0.310896i \(-0.100629\pi\)
\(770\) −10565.7 −0.000642200
\(771\) −2.49140e6 1.07529e7i −0.150941 0.651464i
\(772\) 4.81179e6 0.290578
\(773\) 2.07427e7 1.24858 0.624289 0.781194i \(-0.285389\pi\)
0.624289 + 0.781194i \(0.285389\pi\)
\(774\) 1.86637e7 9.13916e6i 1.11981 0.548345i
\(775\) 2.75823e7 1.64959
\(776\) 8.07315e6 0.481270
\(777\) −4.02141e6 + 931740.i −0.238960 + 0.0553659i
\(778\) 2.22933e7i 1.32046i
\(779\) −4.02506e6 −0.237645
\(780\) 3313.97 767.829i 0.000195035 4.51885e-5i
\(781\) 2.27708e7i 1.33583i
\(782\) 1.55558e7 + 8.93868e6i 0.909654 + 0.522705i
\(783\) 3.45325e6 + 4.24394e6i 0.201291 + 0.247380i
\(784\) −1.96750e6 −0.114320
\(785\) 13375.4i 0.000774696i
\(786\) −1.22682e6 + 284247.i −0.0708310 + 0.0164112i
\(787\) 1.91540e7i 1.10236i −0.834386 0.551180i \(-0.814178\pi\)
0.834386 0.551180i \(-0.185822\pi\)
\(788\) 9.43940e6i 0.541538i
\(789\) −1.22889e7 + 2.84726e6i −0.702779 + 0.162830i
\(790\) −2579.74 −0.000147064
\(791\) 3.91826e7i 2.22665i
\(792\) 3.51905e6 + 7.18648e6i 0.199348 + 0.407102i
\(793\) 1.41124e7i 0.796927i
\(794\) 1.31433e7i 0.739866i
\(795\) 8091.15 1874.68i 0.000454038 0.000105198i
\(796\) 1.24392e6i 0.0695838i
\(797\) 7.92762e6 0.442076 0.221038 0.975265i \(-0.429055\pi\)
0.221038 + 0.975265i \(0.429055\pi\)
\(798\) −721514. 3.11407e6i −0.0401086 0.173109i
\(799\) 1.71934e6i 0.0952783i
\(800\) 3.20000e6i 0.176777i
\(801\) −2.54297e7 + 1.24523e7i −1.40042 + 0.685755i
\(802\) 2.98513e6i 0.163880i
\(803\) −1.89187e7 −1.03539
\(804\) 3.72852e6 + 1.60924e7i 0.203421 + 0.877971i
\(805\) −11292.7 6489.00i −0.000614197 0.000352930i
\(806\) 1.46792e7i 0.795912i
\(807\) 5.57010e6 + 2.40407e7i 0.301078 + 1.29946i
\(808\) 8.40648e6 0.452987
\(809\) 3.14727e7i 1.69068i −0.534226 0.845342i \(-0.679397\pi\)
0.534226 0.845342i \(-0.320603\pi\)
\(810\) −6120.46 4750.96i −0.000327772 0.000254430i
\(811\) 2.15848e7 1.15238 0.576191 0.817315i \(-0.304539\pi\)
0.576191 + 0.817315i \(0.304539\pi\)
\(812\) 3.61680e6 0.192502
\(813\) −1.10162e7 + 2.55240e6i −0.584529 + 0.135432i
\(814\) 3.48238e6 0.184211
\(815\) −5533.11 −0.000291793
\(816\) 6.87319e6 1.59248e6i 0.361354 0.0837239i
\(817\) 7.00336e6 0.367072
\(818\) 1.45013e7i 0.757748i
\(819\) −6.95380e6 1.42008e7i −0.362253 0.739780i
\(820\) 6449.22i 0.000334945i
\(821\) 3.19922e7i 1.65648i 0.560373 + 0.828240i \(0.310658\pi\)
−0.560373 + 0.828240i \(0.689342\pi\)
\(822\) −621252. 2.68134e6i −0.0320692 0.138411i
\(823\) 2.18883e7 1.12645 0.563225 0.826304i \(-0.309561\pi\)
0.563225 + 0.826304i \(0.309561\pi\)
\(824\) −3.92482e6 −0.201373
\(825\) 2.44175e7 5.65741e6i 1.24901 0.289389i
\(826\) 4.93628e6i 0.251738i
\(827\) −91163.8 −0.00463510 −0.00231755 0.999997i \(-0.500738\pi\)
−0.00231755 + 0.999997i \(0.500738\pi\)
\(828\) −652442. + 9.84223e6i −0.0330724 + 0.498905i
\(829\) 2.22385e7 1.12388 0.561939 0.827179i \(-0.310056\pi\)
0.561939 + 0.827179i \(0.310056\pi\)
\(830\) 8564.46i 0.000431524i
\(831\) 1.45732e7 3.37654e6i 0.732070 0.169617i
\(832\) −1.70303e6 −0.0852931
\(833\) 1.35876e7 0.678471
\(834\) 559206. + 2.41354e6i 0.0278392 + 0.120155i
\(835\) 13812.3i 0.000685565i
\(836\) 2.69666e6i 0.133447i
\(837\) 2.59336e7 2.11019e7i 1.27953 1.04114i
\(838\) 1.32393e6i 0.0651259i
\(839\) −2.09955e7 −1.02972 −0.514862 0.857273i \(-0.672157\pi\)
−0.514862 + 0.857273i \(0.672157\pi\)
\(840\) −4989.57 + 1156.06i −0.000243986 + 5.65303e-5i
\(841\) 1.84249e7 0.898285
\(842\) −386470. −0.0187860
\(843\) 1.87667e7 4.34814e6i 0.909533 0.210734i
\(844\) −6.52877e6 −0.315482
\(845\) −6508.87 −0.000313591
\(846\) 848954. 415713.i 0.0407810 0.0199695i
\(847\) 1.62261e7i 0.777151i
\(848\) −4.15800e6 −0.198561
\(849\) 7.54223e6 + 3.25524e7i 0.359113 + 1.54994i
\(850\) 2.20994e7i 1.04914i
\(851\) 3.72200e6 + 2.13873e6i 0.176178 + 0.101235i
\(852\) −2.49149e6 1.07533e7i −0.117587 0.507509i
\(853\) −1.89532e7 −0.891888 −0.445944 0.895061i \(-0.647132\pi\)
−0.445944 + 0.895061i \(0.647132\pi\)
\(854\) 2.12479e7i 0.996946i
\(855\) −1148.32 2345.06i −5.37215e−5 0.000109708i
\(856\) 5.48955e6i 0.256066i
\(857\) 3.22040e7i 1.49781i 0.662676 + 0.748906i \(0.269421\pi\)
−0.662676 + 0.748906i \(0.730579\pi\)
\(858\) 3.01085e6 + 1.29949e7i 0.139628 + 0.602636i
\(859\) −1.79382e7 −0.829462 −0.414731 0.909944i \(-0.636124\pi\)
−0.414731 + 0.909944i \(0.636124\pi\)
\(860\) 11221.2i 0.000517362i
\(861\) 2.92035e7 6.76630e6i 1.34254 0.311060i
\(862\) 1.09686e7i 0.502786i
\(863\) 1.17289e7i 0.536083i −0.963407 0.268041i \(-0.913624\pi\)
0.963407 0.268041i \(-0.0863764\pi\)
\(864\) 2.44816e6 + 3.00872e6i 0.111572 + 0.137119i
\(865\) 16035.1i 0.000728669i
\(866\) −3.00756e6 −0.136276
\(867\) −2.59044e7 + 6.00193e6i −1.17038 + 0.271171i
\(868\) 2.21013e7i 0.995676i
\(869\) 1.01158e7i 0.454414i
\(870\) 2878.15 666.853i 0.000128919 2.98698e-5i
\(871\) 2.75368e7i 1.22990i
\(872\) −1.13404e7 −0.505052
\(873\) −1.34805e7 2.75294e7i −0.598646 1.22253i
\(874\) −1.65618e6 + 2.88221e6i −0.0733378 + 0.127628i
\(875\) 32085.9i 0.00141675i
\(876\) −8.93421e6 + 2.07001e6i −0.393365 + 0.0911407i
\(877\) −2.08107e7 −0.913665 −0.456833 0.889553i \(-0.651016\pi\)
−0.456833 + 0.889553i \(0.651016\pi\)
\(878\) 2.57686e7i 1.12812i
\(879\) −3.73816e7 + 8.66113e6i −1.63187 + 0.378096i
\(880\) 4320.76 0.000188085
\(881\) 1.11999e6 0.0486154 0.0243077 0.999705i \(-0.492262\pi\)
0.0243077 + 0.999705i \(0.492262\pi\)
\(882\) 3.28531e6 + 6.70915e6i 0.142202 + 0.290399i
\(883\) 1.80864e7 0.780640 0.390320 0.920679i \(-0.372364\pi\)
0.390320 + 0.920679i \(0.372364\pi\)
\(884\) 1.17612e7 0.506199
\(885\) 910.133 + 3928.15i 3.90613e−5 + 0.000168589i
\(886\) 2.33164e7 0.997877
\(887\) 47004.2i 0.00200598i −0.999999 0.00100299i \(-0.999681\pi\)
0.999999 0.00100299i \(-0.000319262\pi\)
\(888\) 1.64453e6 381029.i 0.0699856 0.0162153i
\(889\) 949342.i 0.0402873i
\(890\) 15289.2i 0.000647009i
\(891\) 1.86297e7 2.39999e7i 0.786163 1.01278i
\(892\) −1.55707e7 −0.655231
\(893\) 318562. 0.0133680
\(894\) 1.89883e6 + 8.19539e6i 0.0794588 + 0.342946i
\(895\) 479.052i 1.99906e-5i
\(896\) 2.56411e6 0.106701
\(897\) −4.76291e6 + 1.57382e7i −0.197647 + 0.653092i
\(898\) −1.23343e7 −0.510414
\(899\) 1.27488e7i 0.526100i
\(900\) 1.09120e7 5.34334e6i 0.449052 0.219891i
\(901\) 2.87154e7 1.17843
\(902\) −2.52891e7 −1.03494
\(903\) −5.08123e7 + 1.17729e7i −2.07372 + 0.480469i
\(904\) 1.60235e7i 0.652133i
\(905\) 18317.7i 0.000743446i
\(906\) −6.99789e6 3.02030e7i −0.283235 1.22245i
\(907\) 4.52552e7i 1.82663i 0.407256 + 0.913314i \(0.366486\pi\)
−0.407256 + 0.913314i \(0.633514\pi\)
\(908\) −1.31140e7 −0.527863
\(909\) −1.40371e7 2.86660e7i −0.563466 1.15069i
\(910\) −8538.01 −0.000341785
\(911\) 4.14032e7 1.65287 0.826434 0.563033i \(-0.190366\pi\)
0.826434 + 0.563033i \(0.190366\pi\)
\(912\) 295058. + 1.27348e6i 0.0117468 + 0.0506995i
\(913\) −3.35834e7 −1.33336
\(914\) 7.53626e6 0.298394
\(915\) 3917.62 + 16908.5i 0.000154692 + 0.000667656i
\(916\) 1.01433e7i 0.399430i
\(917\) 3.16073e6 0.124127
\(918\) −1.69072e7 2.07784e7i −0.662162 0.813777i
\(919\) 4.19178e6i 0.163723i −0.996644 0.0818615i \(-0.973913\pi\)
0.996644 0.0818615i \(-0.0260865\pi\)
\(920\) 4618.07 + 2653.63i 0.000179883 + 0.000103365i
\(921\) −9.11844e6 + 2.11269e6i −0.354219 + 0.0820706i
\(922\) 1.10757e6 0.0429087
\(923\) 1.84008e7i 0.710940i
\(924\) −4.53319e6 1.95654e7i −0.174672 0.753890i
\(925\) 5.28765e6i 0.203193i
\(926\) 9.59155e6i 0.367588i
\(927\) 6.55364e6 + 1.33836e7i 0.250486 + 0.511533i
\(928\) −1.47907e6 −0.0563790
\(929\) 4.58157e7i 1.74171i −0.491542 0.870854i \(-0.663566\pi\)
0.491542 0.870854i \(-0.336434\pi\)
\(930\) −4074.95 17587.6i −0.000154495 0.000666805i
\(931\) 2.51754e6i 0.0951925i
\(932\) 2.09344e7i 0.789442i
\(933\) 1.08790e7 + 4.69539e7i 0.409152 + 1.76591i
\(934\) 4.65374e6i 0.174556i
\(935\) −29839.4 −0.00111625
\(936\) 2.84371e6 + 5.80732e6i 0.106095 + 0.216664i
\(937\) 2.80439e7i 1.04349i 0.853101 + 0.521746i \(0.174719\pi\)
−0.853101 + 0.521746i \(0.825281\pi\)
\(938\) 4.14599e7i 1.53859i
\(939\) −2.96366e6 1.27912e7i −0.109689 0.473422i
\(940\) 510.421i 1.88412e-5i
\(941\) 1.71431e6 0.0631124 0.0315562 0.999502i \(-0.489954\pi\)
0.0315562 + 0.999502i \(0.489954\pi\)
\(942\) −2.47683e7 + 5.73868e6i −0.909429 + 0.210710i
\(943\) −2.70292e7 1.55315e7i −0.989815 0.568767i
\(944\) 2.01866e6i 0.0737280i
\(945\) 12273.7 + 15084.0i 0.000447091 + 0.000549461i
\(946\) 4.40014e7 1.59859
\(947\) 2.46149e7i 0.891915i −0.895054 0.445958i \(-0.852863\pi\)
0.895054 0.445958i \(-0.147137\pi\)
\(948\) −1.10683e6 4.77712e6i −0.0400002 0.172642i
\(949\) −1.52880e7 −0.551042
\(950\) 4.09461e6 0.147199
\(951\) 1.08037e7 + 4.66289e7i 0.387365 + 1.67188i
\(952\) −1.77079e7 −0.633249
\(953\) −4.27314e7 −1.52410 −0.762052 0.647516i \(-0.775808\pi\)
−0.762052 + 0.647516i \(0.775808\pi\)
\(954\) 6.94300e6 + 1.41787e7i 0.246988 + 0.504391i
\(955\) 341.331 1.21106e−5
\(956\) 6.45642e6i 0.228479i
\(957\) 2.61490e6 + 1.12860e7i 0.0922944 + 0.398344i
\(958\) 9.53864e6i 0.335794i
\(959\) 6.90812e6i 0.242557i
\(960\) 2040.45 472.762i 7.14575e−5 1.65563e-5i
\(961\) 4.92750e7 1.72115
\(962\) 2.81407e6 0.0980387
\(963\) −1.87193e7 + 9.16641e6i −0.650465 + 0.318518i
\(964\) 1.01631e6i 0.0352235i
\(965\) −9865.16 −0.000341025
\(966\) 7.17112e6 2.36957e7i 0.247254 0.817010i
\(967\) 7.40403e6 0.254626 0.127313 0.991863i \(-0.459365\pi\)
0.127313 + 0.991863i \(0.459365\pi\)
\(968\) 6.63555e6i 0.227609i
\(969\) −2.03769e6 8.79471e6i −0.0697153 0.300893i
\(970\) −16551.6 −0.000564822
\(971\) −4.58980e7 −1.56223 −0.781117 0.624385i \(-0.785350\pi\)
−0.781117 + 0.624385i \(0.785350\pi\)
\(972\) 6.17179e6 1.33722e7i 0.209530 0.453979i
\(973\) 6.21819e6i 0.210563i
\(974\) 4.55002e6i 0.153679i
\(975\) 1.97315e7 4.57169e6i 0.664735 0.154016i
\(976\) 8.68919e6i 0.291981i
\(977\) 2.13083e6 0.0714187 0.0357093 0.999362i \(-0.488631\pi\)
0.0357093 + 0.999362i \(0.488631\pi\)
\(978\) −2.37398e6 1.02461e7i −0.0793650 0.342541i
\(979\) −5.99529e7 −1.99919
\(980\) 4033.77 0.000134167
\(981\) 1.89361e7 + 3.86706e7i 0.628229 + 1.28295i
\(982\) 5.65072e6 0.186993
\(983\) −4.68620e7 −1.54681 −0.773404 0.633913i \(-0.781448\pi\)
−0.773404 + 0.633913i \(0.781448\pi\)
\(984\) −1.19426e7 + 2.76703e6i −0.393197 + 0.0911018i
\(985\) 19352.7i 0.000635552i
\(986\) 1.02145e7 0.334600
\(987\) −2.31130e6 + 535516.i −0.0755202 + 0.0174976i
\(988\) 2.17914e6i 0.0710220i
\(989\) 4.70291e7 + 2.70238e7i 1.52889 + 0.878529i
\(990\) −7214.78 14733.8i −0.000233957 0.000477778i
\(991\) 2.45529e7 0.794180 0.397090 0.917780i \(-0.370020\pi\)
0.397090 + 0.917780i \(0.370020\pi\)
\(992\) 9.03817e6i 0.291609i
\(993\) −2.58619e7 + 5.99207e6i −0.832314 + 0.192843i
\(994\) 2.77046e7i 0.889376i
\(995\) 2550.29i 8.16641e-5i
\(996\) −1.58595e7 + 3.67457e6i −0.506573 + 0.117370i
\(997\) −5.51484e7 −1.75710 −0.878548 0.477655i \(-0.841487\pi\)
−0.878548 + 0.477655i \(0.841487\pi\)
\(998\) 2.68800e7i 0.854284i
\(999\) −4.04533e6 4.97159e6i −0.128245 0.157609i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 138.6.d.a.137.10 yes 40
3.2 odd 2 inner 138.6.d.a.137.11 yes 40
23.22 odd 2 inner 138.6.d.a.137.9 40
69.68 even 2 inner 138.6.d.a.137.12 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.6.d.a.137.9 40 23.22 odd 2 inner
138.6.d.a.137.10 yes 40 1.1 even 1 trivial
138.6.d.a.137.11 yes 40 3.2 odd 2 inner
138.6.d.a.137.12 yes 40 69.68 even 2 inner